Stochastic continuum approach to high-cycle fatigue: Modelling stress history as a stochastic process

Tero Frondelius, Terhi Kaarakka, Reijo Kouhia, Jari Mäkinen, Heikki Orelma, Joona Vaara

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In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, Stenström and Ristinmaa in 2008, is extended to cases where the stress history is a stochastic process. The basic three-parameter Ornstein–Uhlenbeck process is chosen for stress description. As a practical example, the theory is applied in both finite and infinite life cases. A definition for the safety factor is introduced, which is reduced to a minimization problem of the value for the endurance surface. In the stochastic case, the values of the endurance surface form a stochastic process and the cumulative distribution function can be constructed for its maximum values.

Original languageEnglish
Article number104454
JournalEuropean Journal of Mechanics, A/Solids
Early online date6 Nov 2021
Publication statusPublished - 2022
Publication typeA1 Journal article-refereed


  • High-cycle fatigue
  • Lifetime distribution
  • Ornstein–Uhlenbeck process
  • Out-of-phase loading
  • Safety factor distribution
  • Stochastic loading

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)


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